NDA MATHEMATICS QUIZ-3

In the expansion of $\left(a+a^{-2}\right)^{n-3}$ there will be a term containing a $2 \mathrm{r}$. If

If the vector $\vec{r}=x \vec{\imath}+y \vec{\jmath}+2 \vec{k}$ makes an obtuse angle with the axis of with having direction cosines as $l, \frac{1}{2} \sqrt{2} \frac{1}{2} \sqrt{2}$ then the angle made by the vector with the $\mathrm{x}$ - axis will be

In which interval the function $f(x)=\frac{x}{\log x}$ decreases.

Value of the integral $\int \frac{\left(e^{x}\right) d x}{\left(e^{x}-2\right)\left(e^{2 x}-4 e^{x}+5\right)}$ is:

In a triangle $A B C \quad b=\sqrt{3}+1$, $c=\sqrt{3}-1$ and $A=60^{\circ}$ than angle $C$ will be.

Tangent to the curve $x=\mathrm{a} \sqrt{\cos 2 \theta} . \sin \theta ; \mathrm{y}=$ a $\sqrt{\cos 2 \theta} \cos \theta$ is perpendicular to $x$ - axis then value of $\theta$ will be.....

Roots of the equation $\alpha(\beta-\lambda) x^{2}+\beta(\lambda-\alpha) x+$ $\lambda(\alpha-\beta)=0$ are equal, then $\alpha, \beta, \lambda$ are in:

If $g(x)=\frac{1}{1-x}$ then go go $g$ is

If $|\vec{a}|=3$ and $|\vec{b}|=2$ and $3 \bar{a}+\bar{b}=\sqrt{85}=1$

than $[|3 \vec{a}+\vec{b}|]^{2}$ equals

The intercepts made by a plane on the coordinate axes are in the ratio 2: 3: 4. If the plane passes through (5, 0, –2) its equation will be.